It's the election night scenario some fear: one candidate wins the popular vote, while the other wins the electoral college. Our founding fathers in their genius or lack thereof decided against Americans directly electing their presidents. As Al Gore learned, a popular vote victory without a coinciding electoral college win is worthless.

But we shouldn't rush to assumptions about dead heats and tied results yet. Jon Bernstein reminds us not to read too much into the discrepancy between electoral college projections and popular vote polling. State polls (on which electoral college extrapolations are based) are taken far less frequently than national polls, and therefore lag considerably. There are fewer pollsters surveying individual states, which means that some pollsters who might consistently lean, for whatever reason, towards the Republicans or Democrats are weighted more heavily in state polling averages. Right now, for instance, the last two polls in Colorado have a tied race and a 13-point Obama lead respectively.

Still, that doesn't keep me from bouncing electoral college scenarios around in my head. I wonder what the chances are that either Barack Obama or Mitt Romney wins the popular vote, but not the electoral college (a scenario known as an "electoral college inversion").

In 2008, Obama took the electoral college with room to spare. And, of course, he won the popular vote nationally by 7.3 points. Even if you subtract 7.3 percentage points from Obama's margin of victory in the states he won, he still would have taken the electoral college, with 272 electoral votes. In fact, you would have had to subtract 9 points from all the states Obama took in order for McCain to have won the electoral college. (This 9 points represents Obama's margin in Colorado, the tipping-point state which gave him his electoral college majority.)

The 1.7-point difference between Obama's margin in the national vote and his share of the vote in the tipping-point state is quite enormous if you think about it. The margin between Gore and Bush nationally in 2000 was only 0.5 percentage points, while Florida was a statistical tie.

Many Democrats might be counting on this sort of divergence to occur again. Not me. For one thing, John McCain's campaign was greatly outspent and outstaffed on the ground in a number of swing states. Seth Masket determined that Obama was able to drive up his margins in many swing states and probably won the closest ones, like Indiana and North Carolina, because of this advantage. In 2012, though, thanks to an assist from outside organizations, Romney's going to have the resources necessary to compete – and probably completely level the field – with Obama.

We also don't know how states will move relative to the popular vote. Nate Silver took a stab at this in his "elasticity" project this week to try to figure how states will move relative to changes in the national vote. His study was based on 2008 exit poll data to determine swing voters, and we simply don't know yet if this approach will hold for the 2012 election. Still, I would certainly agree that states like Iowa, New Hampshire, and Wisconsin are primed to move heavily towards the Republicans this election.

Obamahas maintained his edge among Latinos and especially black voters. He has, however, seen major losses among whites and especially the white working class. Certain swing states, such as North Carolina and Virginia, have a lot of African Americans and relatively few white working-class voters compared to the nation. Others such as Iowa, Michigan, Minnesota, New Hampshire, Oregon, and Wisconsin have a ton of white working-class voters. We've already seen Obama's lead in the heavily polled state of Wisconsin disappear – despite the fact that he won it by 13.9 points last time.

My co-blogger at Margin of Error, Brice Acree, tested who would likely win if the national vote were a tie, but using a different and more realistic model than a uniform national vote swing. He estimated how the electoral college would break down if the current polls are correct: Obama maintains his 2008 level of support among blacks and Latinos, but he loses so much support among white voters that the popular vote ends up as a tie. Acree found that under this scenario, it would actually be Mitt Romney who would win more often. The margin of error on such estimates is obviously huge, but it makes the larger point that we cannot make many assumptions about who would benefit in a split between the electoral college and popular vote.

But let's get down to the nitty-gritty, what is the chance of an electoral college inversion? Nicholas Miller studied (pdf) past election results and estimated there to be between 3% and 5%, which matches the findings of the respected Sam Merrill. The higher percentage includes the taking into account of results from the Jim Crow era, when Democratic votes were heavily concentrated in the south.

The chance of an inversion expectedly goes up as the election result gets closer. In a popular vote tie, the chance is 50%. With a 1 percentage point margin, it decreases to 25%. A 2-point margin decreases the chance to about 12.5%. Any margin beyond 4 points makes the possibility of an inversion approach zero.

Most polls of this year's presidential election are closer than 4 points. That suggests that there is at least some chance that one of these candidates could win the popular vote, but not the electoral college. But only as we close on 6 November will we get an idea of the exact chance of an electoral college inversion and who it might benefit.